A sinusoidal wave travels along a stretched string. A particle on the string has a maximum velocity of \(1.40 \mathrm{~m/s}\) and a maximum acceleration of \(270 \mathrm{~m/s^2}\text{.}\) Find the frequency and amplitude of the wave.
Represent the situation physically. A history graph of the wave can be seen below. The maximum speed happens when the displacement is zero, and the maximum acceleration happens when the displacement is at a maximum
Is your numerical answer reasonable? This string has a frequency of 30 Hertz. For a string with this frequency, it is not surprising the maximum displacement is only a few millimeters. This could likely be built in a lab, so these numbers do seem reasonable.
If the maximum speed increases, the frequency decreases and the displacement increases. With more speed, a particle on the string is travelling faster up and down in a larger period.
During takeoff, the sound intensity level of a jet engine is \(150 \mathrm{~dB}\) at a distance of \(22 \mathrm{~m}\text{.}\) What is the sound intensity level at a distance of \(1.0 \mathrm{~km}\text{?}\)
Waves A and B are traveling in the same medium, and they have the same wavelength and frequency. But Wave A has an amplitude twice that of Wave B. How does the speed of Wave A compare to the speed of wave B?
Sitting on the dock of the bay, you notice that the crests of an ocean wave pass a pier every \(12.0 \mathrm{~s}\text{.}\) You know also that there are two buoys \(28 \mathrm{~m}\) apart, and that the crest travels between the buoys in about \(5 \mathrm{~s}\text{.}\) What is the wavelength of the ocean wave?
Consider a logarithmic function like that found in the equation for decibels (also used for the Richter scale, by the way). If the sound intensity level increases from 30 dB to 60 dB, what can you say about the intensity of the wave?
If the sound intensity level at a certain point increases from \(30 \mathrm{~dB}\) to \(60 \mathrm{~dB}\text{,}\) by what factor did the intensity change?
You are attending a concert by your favorite band, but you can barely hear them, because only 2 of the 20 speakers are working. The sound intensity level at your location is \(60 \mathrm{~dB}\text{.}\) If all 20 speakers suddenly start working, what is the new sound intensity level at your location? Assume that you don’t change your location and that all of the speakers are the same distance from you.
Dolphins emit clicks of sound for communicating and echo-location. A marine biologist, standing at rest in shallow seawater, is monitoring a dolphin swimming directly away at 8 m/s. The biologist measures the number of clicks occurring per second to be at a frequency of 2500 Hz. The speed of sound in calm seawater is 1522 m/s. What is the frequency of the clicks that the dolphin sends out?
