# Vibrations, Waves, and Sound

Please solve the following problems. You must show all work for full/partial credit. When complete, attach a typed cover sheet and submit to the assignment drop-box.

1. A spring with negligible mass stretches 34.0 cm when a 144 g gram mass is suspended from it. Now I suspend a mass m from the spring. If it oscillates at an angular frequency of 4.51 rad/s, what is the mass?

2. A 3.45 kg mass vertically compresses a spring 67.0 cm before it starts to rebound. How high will the mass move above the uncompressed spring if it the mass is left to “bounce” back up?

3. A transverse traveling wave on a cord is represented by D = 0.25 sin (6.8x + 28t) where D and x are in meters and t is in seconds.

a) Determine the wavelength of this wave.

b) Determine the frequency of this wave.

c) Determine the speed of this wave.

d) Determine the amplitude of this wave.

f) Determine maximum and minimum speeds of particles of the cord.

4. A person is watching water waves at the ocean and they notice the peak to peak distance between the waves is 3.4 m. They also notice there are 55 waves every 10.0 seconds passing the end of a pier. How fast are the waves going?

5. A whale sends an undersea signal to its mate and then gets a response 4.5 seconds later. How far away is the whale’s mate?

6. A person sees a distant lightning strike, then 4.5 seconds later he hears the thunder clap. If it is 35 degrees Celsius, how far away was the lightning strike?

7. A single bass amplifier produces a volume of 102 dB. What is the sound level if the guitar amplifier that produces 98dB is played at the same time as the bass amplifier?

8. A string on a guitar vibrates at 420 Hz. If the tension on the string is 102 N, what is the mass of the string if the portion that vibrates is 63.7 cm long?

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