11. Two waves of equal amplitude and frequency of 170 Hz travel with a speed of 85.0 m/s in opposite directions in a string that is fixed at both ends. If the string is 1.25 m long, which harmonic mode (n) is the standing wave set up in the string?

1. A string fixed on both ends is 5.5 m long and has a mass of 0.17 kg. The tension if the string is 70 N. The string is vibrating to produce a standing wave at the fundamental frequency of the string. (a) What is the speed of the waves on the string? V = V m/s (b) What is the wavelength of the standing wave produced? m (c) What is the period of the standing wave? T=

10. A rubber ducky (located at x = 0 m) that floats on a lake and bobs up and \y (in cm) at t=0 down due to one dimensional water waves. Shown are a y(x) graph that depicts the water wave as a function of position at the time t = 0 s and a y(t) graph that depicts the vertical displacement of rubber ducky as a function of time. 4 At 2 x (in m) 3 -4 In this question you are to assume that you are trying to fit the general equation for a travelling sine wave given by: -6 y (in cm) at x=0 y(x,t) = A sin 27÷±27; 6 t (in s) -2 -4 -6 a. What is the wavelength (in m) and period (in s) of this water wave? b. What is the velocity of this water wave (both speed and direction)? c. What is the value of ø (i.e. the phase constant) for this water wave (in radians)?

The transverse displacement of a stretched string from equilibrium as a function of time and position is given by: Evaluate y%30.13cos(9 x + 27 t). x and y are in m; t is in s. The wave moves in the positive x direction. The speed of the wave is v The wavelength is ..... 1 m. The period is ..... 0.1 seconds. False False ..... 4 m/s. False False A traveling wave can be any function of (2*pi*x/lamda-2*pi*t/period). Calculate the various parameters where needed then select the proper answers. Submit Answer Incorrect. Tries 1/12 Previous Tries Calculate the average power transmitted by the string. Data: mass of a 207 m long piece of the string is 2.59 kg. Submit Answer Tries 0/12 Post Discussion Senc

1. Consider two sinusoidal waves traveling along a string, modeled as y,(x,t) = (0.3m)sin([4m]x+[3s¯]t) and y2(x,t) = (0.6m)sin(18mx-[6s '1). What is the height of the resultant wave formed by the interference of the two waves at the position x=1.1 m at time t=0.6 s? y(1.1 m, 0.6 s) = Note: Assume the phase is in radians.

12. In the arrangement shown, a mass can be hung from a string (with a linear mass density of H = 0.002 */m) that passes over a massless pulley. The string is connected to an oscillator of constant frequency f. The length of the string between the oscillator and pulley is L = 2.00 m. When the mass is either 16 kilograms or 25 kilograms, standing waves are observed; however, no standing waves are observed with any mass between these values. (a) What is the frequency of the oscillator? (hint: the heavier the mass, the fewer the number of nodes) (b) What is the largest mass for which standing waves can be observed? L f 11 w 11 oto o onstont

4. A travelling wave on a string is given by: = 5.7(cos(3.3x) cos(4.4t) – sin(3.3x) sin(4.4t)) y = For this wave find (a) its velocity of propagation (b) the transverse velocity (c) the transverse acceleration (d) the maximum displacement, velocity and acceleration of a particle on the string.

5) What tension is needed to make a 1.2m long string resonate at its fourth harmonic with a frequency of 240Hz? The linear density of the string is 1.55 g/m .

5. On a day when the speed of sound in air is 345 m/s, the fundamental frequency of an open-ended organ pipe is 690 Hz. If the second harmonic of this pipe has the same wavelength as the second overtone (third harmonic) of a closed-end pipe, what is the length of each pipe?