Find the three longest wavelengths (call them A₁, A₂, and A3) that "fit" on the string, that is, those that satisfy the boundary conditions at z = 0 and L. These longest wavelengths have the lowest frequencies. Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas. ▸ View Available Hint(s) A₁, A2, A3 = Submit Part D - ΓΙ ΑΣΦ 3 ? The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength ₁ Find the frequency f; of the th normal mode. Express f; in terms of its particular wavelength X, and the speed of propagation of the wave v.

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

A radio wave of wavelength 21.5 cm passes through a window of width 96.3 cm. a. What is the angular separation of the first-order minima? b. How does your answer change for a radio wave of twice the wavelength?

Two radio antennas separated by d = 300 m as shown in Figure P27.3 simultaneously broadcast identical signals at the same wavelength. A car travels due north along a straight line at position x = 1 000 m from the center point between the antennas, and its radio receives the signals. (a) If the car is at the position of the second maximum after that at point O when it has traveled a distance y = 400 m northward, what is the wavelength of the signals? (b) How much farther must the car travel from this position to encounter the next minimum in reception? Note: Do not use the small-angle approximation in this problem.

Consider a sound wave moving through the air modeled with the equation s(x,t)=6.00nmcos(54.93m1x18.84103s1t) . What is the shortest time required for an air molecule to move between 3.00 nm and -3.00 nm?

(a) What is the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter? (b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be? (c) How big a spot would be illuminated on the moon, neglecting atmospheric effects? (This might be done to hit a corner reflector to measure the round-trip time and, hence, distance.)

Radio station WWVB, operated by the National Institute of Standards and Technology (NIST) from Fort Collins, Colorado, at a low frequency of 60 kHz, broadcasts a time synchronization signal whose range covers the entire continental US. The timing of the synchronization signal is controlled by a set of atomic clocks to an accuracy of 101012 s, and repeats every 1 minute. The signal is used for devices, such as radio-controlled watches, that automatically synchronize with it at preset local times. WWVB's long wavelength signal tends to propagate close to the ground. (a) Calculate the wavelength of the radio waves from WWVB. (b) Estimate the error that the travel time of the signal causes in synchronizing a radio controlled watch in Norfolk, Virginia, which is 1570 mi (2527 km) from Fort Collins, Colorado.

(a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light? (b) For all visible light?

Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.

Consider two waves y1(x,t) and y2(x,t) that are identical except for a phase shift propagating in the same medium. (a)What is the phase shift, in radians, if the amplitude of the resulting wave is 1.75 times the amplitude of the individual waves? (b) What is the phase shift in degrees? (c) What is the phase shift as a percentage of the individual wavelength?