Concept explainers
(a)
The expression for the radius of the sphere in the water.
(a)
Answer to Problem 73AP
The expression for the radius of the sphere in the water is
Explanation of Solution
Write the expression for tension in the string (Refer Figure 18.11a).
Here,
Write the expression for tension on the string included the buoyant force on the sphere (Refer Figure 18.11b).
Here,
Write the expression for the buoyant force acts on the sphere.
Here,
Write the expression for volume of the sphere.
Here,
Write the expression for the frequency of the oscillation.
Here,
Write the expression for the fundamental frequency of the oscillation.
Write the expression for frequency of the two antinodes formed on the string.
Conclusion:
Substitute the equation (III) and (IV) in equation (II).
Rewrite the equation (V) and (VI).
Substitute equation (I) in the above equation.
Substitute equation (VII) in the above equation.
Solve the above relation for radius.
Substitute
Therefore, the expression for the radius of the sphere in the water is
(b)
The minimum allowed value of n.
(b)
Answer to Problem 73AP
The minimum allowed value of n is
Explanation of Solution
The factor inside the cubic root is,
Conclusion:
Since the above factor will be either zero or negative which are meaningless results, for
Therefore, the minimum allowed value of n is
(c)
The radius of the largest sphere producing a standing wave on the string.
(c)
Answer to Problem 73AP
The radius of the largest sphere producing a standing wave on the string is
Explanation of Solution
The mass of the sphere is held constant while its radius is changed, there will reach a point where the density of the sphere reaches the density of the water, and then the sphere will float on the water.
Write the expression for the density of the sphere.
Here,
Rearrange the above solution for r.
Conclusion:
Substitute
Therefore, the radius of the largest sphere producing a standing wave on the string is
(d)
Can larger sphere is used, what will happen.
(d)
Answer to Problem 73AP
The sphere floats on the water.
Explanation of Solution
The mass of the sphere is held constant while its radius is changed, it will reach a point where the density of the sphere reaches the density of the water, and then the sphere will float on the water.
Conclusion:
If the large sphere is used, then the sphere will float on the water.
Want to see more full solutions like this?
Chapter 18 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
- Consider detectors of water waves at three locations A, B, and C in Active Figure 13.23b. Which of the following statements is true? (a) The wave speed is highest at location A. (b) The wave speed is highest at location C. (c) The detected wavelength is largest at location B. (d) The detected wavelength is largest at location C. (e) The detected frequency is highest at location C. (f) The detected frequency is highest at location A.arrow_forwardLet us assume we are using SI units (kg, m, s). Consider the harmonic travelling wave 17 y(x, t) = = 12 cos(3x - 12πt). Assume the above harmonic wave is a solution of the motion of a string with tension T = 1 Newton. What is the string's density?p= kg/m What is its kinetic energy density? What is its kinetic energy over one wavelength? Ek What is its potential energy density? What is its potential energy over one wavelength? Ey = J/m J/marrow_forwardA wire is under tension due to hanging mass. The observed wave speed is 24 m/s when the suspended mass is 3kg. a) what is the string's linear density ? b) if the length of the vibrating portion of the string is 1.2m, what is the frequency?arrow_forward
- Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density ? , and fluid viscosity ? . Manipulate your Π’s to get the parameters into the following formarrow_forwardOn a certain guitar, the string is 61.4 cm long and has a linear mass density of 0.00525 g/cm. The fundamental frequency vibrates at 236 Hz. a) What is the velocity of the transverse waves in the string?b) What is the tension in the rope?c) What will be the frequency of the 4th harmonic if the voltage is multiplied by 2?arrow_forwardA violin string of ?=31.8 cm in length and ?=0.64gm⁄ linear mass density is tuned to play an A4 note at 440.0 Hz. This means that the string is in its fundamental oscillation mode, i.e., it will be on that note without placing any fingers on it. From this information, A. Calculate the tension on the string that allows it to be kept in tune. B. If from the midpoint of the string a maximum transverse motion 2.59 mm is observed when it is in the fundamental mode, what is the maximum speed ?? ?á? of the string's antinode? I need help with the B part please :)arrow_forward
- Consider a 1 meter-long string with a mass of 50 g attached to a string vibrator. The tension in the string is 80 N. When the string vibrator is turned on, it oscillates with a frequency of 64 Hz and produces a sinusoidal wave on the string with an amplitude of 4 cm and a constant wave speed. Give your answers to 3 sig fig. A)VWhat is the linear density of the medium?____kg/m B)What is the wave speed?____m/s C)What is the angular frequency?______Hz D) What is the time-averaged power supplied to the wave by the string vibrator?___Warrow_forwardQuestions 1-6: Consider a wave on a string that can be described by the following equation: y (x, t) = 2.5 cm Sin(2.0 m-1x + 1800 s-1- 4.7) %3D 1. This is describes a... [circle one] ( sanding wave / wave traveling toward +x/wave traveling towards -x) 2. Amplitude = 3. Wavelength = 4. Frequency = 5. Wave speed% = 6. Speed of the medium att = 2.0 ms = X-0.25marrow_forwardSuperposition of sinusoidal waves can lead to non-sinusoidal waves. Evaluate the statement with mathematical proof and the necessary diagram. The fundamental frequency of a certain string wave is 175Hz. Calculate the first 4 harmonic frequencies.arrow_forward
- Chapter 17, Problem 020 The figure shows four isotropic point sources of sound that are uniformly spaced on an x axis. The sources emit sound at the same wavelength and same amplitude sm, and they emit in phase. A point P is shown on the x axis. Assume that as the sound waves travel to P, the decrease in their amplitude is negligible. What multiple of sm is the amplitude of the net wave at P if distance d in the figure is (a)1A, (b)2, and (c)4/? (a) Number (b) Number (c) Number Units Units Units S₁ Sa Sa + S₁arrow_forwardAs we said, sound waves can be modeled with sine waves. The standard musical pitch is the A440 which means that the musical note A4 has a frequency of 440 Hz. So this note oscillates once every seconds and it could be modeled using the curve y = sin(440- 2nt) = sin(880nt). For each of the following musical notes, what would w be if we wanted to model the sound wave with y = sin(wt)? !! %3D (a) (i) C4, (261.63 Hz (iii) E4, (329.63 Hz) (v) G4, (392 Hz) (ii) D4, (293.66 Hz) (iv) F4, (349.23 Hz) (vi) B4, (493.88 Hz)arrow_forwardWS19 (rev. 2.5) Page 71 19. Waves Problems 1. The equation of a certain wave on a string is given by y(x,t) = 0.1 sin{2r(x - 10t)} with x and y in meters, andt in seconds. Which way is the wave moving, to the left or to the right? How do you know? (b) What is the wavelength of the wave? frequency? phase speed? (c) If the string has a mass per unit length of 0.1 kg/m, what is the tension in the string? (d) What is the maximum transverse velocity of the string (that is, the maximum vertical velocity of particles in the cord)? [Ans: (b) 1 m; 10 Hz; 10 m/s; (c) 10 N; (d) 2n m/s] (a) bow doarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University