You are setting up two standing string waves. You have a length of uniform piano wire that is 4.0 m long and has a mass of 0.150 kg. You cut this into two lengths, one of 1.9 m and the other of 2.1 m, and place each length under tension. What should be the ratio of tensions (expressed as short to long) so that their fundamental frequencies are the same?

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A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.10 MHz. The wavelength of the waves in seawater is 7.27×10^{−4} m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.5 s later. How deep is the ocean at that point?

Part A = 0.276ms

Part B = 0.913m/s^{2}

During an earthquake, the floor of an apartment building is measured to oscillate in approximately simple harmonic motion with a period of 1.90 seconds and an amplitude of 8.35 cm.

Determine the maximum speed of the floor during this motion.

Determine the maximum acceleration of the floor during this motion.

Part A = 1.2m/s

Part B = at the equilibrium position

Part C = 1.0m/s

A mass-spring system is in SHM in the horizontal direction. If the mass is 0.25 kg, the spring constant is 15 N/m, and the amplitude is 15 cm, what is the maximum speed of the mass? Where does this occur? What is the speed at a half-amplitude position?

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Part A = 40cm

Part B = 120cm

Part C = 384m/s

Part D = overtone number = pattern number -1

Part E = This is a complex tone with a fundamental of 400 Hz, plus some of its overtones.

Standing waves on a guitar string form when waves traveling down the string reflect off a point where the string is tied down or pressed against the fingerboard. the entire series of distortions may be superimposed on a single figure, like this (intro 2 figure) , indicating different moments in time using traces of different colors or line styles.

What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? How does the overtone number relate to the standing wave pattern number, previously denoted with the variable n?

Part A = See diagram in the Solutions Below

Part B = See diagram in the Solutions Below

At the instant shown, orient v_{A} and v_{B} to correctly represent the direction of the wave velocity at points A and B.

At the instant shown, orient the given vectors v_{A} and v_{B} to correctly represent the direction of the velocity of points A and B.