Resnick & Halliday Solutions for Chapter: Waves-II, Exercise 1: Problems

What is the intensity at radial distances (a) $2.50 \mathrm{m}$, and (b) $6.00 \mathrm{m}$ from an isotropic point source of sound that emits energy at the rate $12.0 \mathrm{W}$. Assuming no energy absorption by the surrounding air?

When you "crack" a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The sudden production of the bubble, called "cavitation" produces a sound pulse-the cracking sound. Assume that the sound is transmitted uniformly in all directions and that it fully passes from the knuckle interior to the outside. If the pulse has a sound level of $50 \mathrm{dB}$ at your ear, estimate the rate at which energy is produced by the cavitation.(Take, the distance between your fingers and ears is approximately $30 \mathrm{cm}$).

A tuning fork of unknown frequency makes $4.00$ beats per second with a standard fork of frequency $384 \mathrm{Hz}$. The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork?

A sound wave of frequency $280 \mathrm{Hz}$ has an intensity of $1.00 \mathrm{\mu W} {\mathrm{m}}^{-2}$. What is the amplitude of the air oscillations caused by this wave? 
Take, Velocity of sound in air $=343 \mathrm{m} {\mathrm{s}}^{-1}$ and Density of air $=1.21 \mathrm{kg} {\mathrm{m}}^{-3}$.

Party hearing. As the number of people at a party increases, you must raise your voice for a listener to hear you against the background noise of the other party goers. However, once you reach the level of yelling, the only way you can be heard is if you move closer to your listener, into the listener's "personal space." Model the situation by replacing you with an isotropic point source of fixed power $\mathrm{P}$ and replacing your listener with a point that absorbs part of your sound waves. These points are initially separated by ${\mathrm{r}}_{\mathrm{i}}=1.20 \mathrm{m}.$ If the background noise increases by $\mathrm{\Delta \beta }=9.0 \mathrm{dB}$ the sound level at your listener must also increase. What separation ${\mathrm{r}}_f$ is then required'?

Two identical piano wires have a fundamental frequency of $600 \mathrm{Hz}$, when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $8.0$ beats per second when both wires oscillate simultaneously?

A sound wave of the form $S=S_{\mathrm{m}}\cos \left(kx-\omega t+\varphi \right)$ travels at $343 \mathrm{m} {\mathrm{s}}^{-1}$ through air in a long horizontal tube. At one instant, air molecule $A$ at $x=2.000 \mathrm{m}$ is at its maximum positive displacement of $5.00 \mathrm{nm}$ and air molecule $B$ at $x=2.070 \mathrm{m}$ is at a positive displacement of $2.00 \mathrm{nm}$. All the molecules between $A$ and $B$ are at intermediate displacements. What is the frequency of the wave?

You have five tuning forks that oscillate at the close but different resonant frequencies. What are (a) the maximum and (b) the minimum number of different beat frequencies you can produce by sounding the forks two at a time, depending on how the resonant frequencies differ?