# Harmonic motion properties

32. A 0.50-kg mass oscillates in simple harmonic motion on a spring with a spring constant of 200 N/m. What are:

a) The period?

b) The frequency of the oscillation?

48. The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin 0.50t. What are the particle's:

a) Displacement?

b) Velocity?

c) Acceleration at t = 1.0 s?

70. A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.50 MHz. The wave-length of the waves in seawater is 4.80 x 10^-4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.0 s later. How deep is the ocean at this point? (Assume the wavelength is constant at all depths.)

90. The fundamental frequency of a stretched string is 100 Hz. What are the frequencies of:

a) The second harmonic?

b) The third harmonic?

100. A 0.10-kg mass suspended on a spring is pulled to 8.0 cm below its equilibrium position and released. When the mass passes through the equilibrium position, it has a speed of 0.40 m/s. What is the speed of the mass when it is 4.0 cm from the equilibrium position?

16. Particles approximately 3.0 x 10^-2 cm in diameter are to be scrubbed loose from machine parts in an aqueous ultrasonic cleaning bath. Above what frequency should the bath be operated to produce wavelengths of this size and smaller?

48. A person standing 4.0 m from a wall shouts such that the sound strikes the wall with an intensity of 2.5 x 10^-4 W/m^2. Assuming that the wall absorbs 20% of the incident energy and reflects the rest, what is the sound intensity level just before and after the sound is reflected?

50. A 1000-Hz tone from a loudspeaker has an intensity level of 100 dB at a distance of 2.5 m. If the speaker is assumed to be a point source, how far from the speaker will the sound have intensity levels:

(a) Of 60 dB?

(b) Barely high enough to be heard?

64. What is the frequency heard by a person driving 50 km/h directly toward a factory whistle (f = 800 Hz) if the air temperature is 0 degrees C?

74. Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving with a speed of 12.0 m/s toward an insect at an air temperature of 20.0 C, :

a) What frequency is heard by the insect?

b) What frequency is heard by the bat from the reflected sound?

c) Would the speed of the bat affect the answers?

#### Solution Summary

The 9-pages solution provides complete step by step explanations and derivations of all important expressions and numerical results.