Vibrations, Waves, and Sound

Please solve the following problems. You must show all work.

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 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 a guitar amplifier what produces 98 dB is played at the same time?

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? 

Notes on Week 6 Homework:

In number 2, assume the mass is release directly above the unstretched spring. The question should give you a pretty simple answer because it doesn’t tell you a  height above the spring. Using the conservation of energy, you should find that the mass doesn’t even matter. 

Part f of number 3 is asking for “speeds” which only refers to the magnitude of the speeds. There shouldn’t be any negative answers.

Remember sound travels at different speeds through different materials.

Sound in water for example does not travel at the same speed as water in air.

Other than that, I’ll just remind you an important hint. Decibels are a logarithmic scale. They do not add together like normal numbers. They’re a made up scale with an arbitrary zero point so you can’t do real math with them unless you use what you know about mathematics for logarithmic functions.