A loudspeaker, mounted on a tall pole, is engineered to emit $75 \%$ of its sound energy into the forward hemisphere, $25 \%$ toward the back. You measure an $85 \mathrm{~dB}$ sound intensity level when standing $3.5 \mathrm{~m}$ in front of and $2.5 \mathrm{~m}$ below the speaker. What is the speaker's power output?

A communications truck with a 44-cm-diameter dish receiver catc on the roof starts out $10 \mathrm{~km}$ from its base station. It drives directly away from the base station at $50 \mathrm{~km} / \mathrm{h}$ for $1.0 \mathrm{~h}$, keeping the receiver pointed at the base station. The base station antenna broadcasts continuously with $2.5 \mathrm{~kW}$ of power, radiated uniformly in all directions. How much electromagnetic energy does the truck's dish receive during that $1.0 \mathrm{~h}$ ?

A snapshot graph at $t=0 \mathrm{~s}$ of two waves approaching each other at $1.0 \mathrm{~m} / \mathrm{s}$. At what time was the snapshot graph?

A bat locates insects by emitting ultrasonic “chirps” and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?

A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. a. What frequency do you hear? b. What frequency does your friend hear if you suddenly start singing at 400 Hz?

A battery-powered siren is attached to the rim of a $20.0$-cm-diameter rotating disk. As the disk spins, you hear the sound varying between $724 \mathrm{~Hz}$ and $778 \mathrm{~Hz}$. What are (a) the siren's frequency and (b) the disk's angular velocity in rpm? The air temperature is $20^{\circ} \mathrm{C}$.

A loudspeaker at the origin emits a 120 Hz tone on a day when the speed of sound is 340 m/s. The phase difference between two points on the x-axis is 5.5 rad. What is the distance between these two points?

a standing wave on a string that is oscillating at $100 \mathrm{~Hz}$. a. How many antinodes will be if the frequency is increased to $200 \mathrm{~Hz}$ ? b. If the tension is increased by a factor of 4 , at what frequency will the string continue to oscillate as a standing wave that looks like the one in the figure?

A starship approaches its home planet at a speed of 0.10c. When it is $54 \times 10^{6}$ km away, it uses its green laser beam ( $\lambda = 540 \text{ nm}^2$ ) to signal its approach. a. How long does the signal take to travel to the home planet? b. At what wavelength is the signal detected on the home planet?

One way to monitor global warming is to measure the average temperature of the ocean. Researchers are doing this by measuring the time it takes sound pulses to travel underwater over large distances. At a depth of $1000 \mathrm{~m}$, where ocean temperatures hold steady near $4^{\circ} \mathrm{C}$, the average sound speed is $1480 \mathrm{~m} / \mathrm{s}$. It's known from laboratory measurements that the sound speed increases $4.0 \mathrm{~m} / \mathrm{s}$ for every $1.0^{\circ} \mathrm{C}$ increase in temperature. In one experiment, where sounds generated near California are detected in the South Pacific, the sound waves travel $8000 \mathrm{~km}$. If the smallest time change that can be reliably detected is $1.0 \mathrm{~s}$, what is the smallest change in average temperature that can be measured?

A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a 1.0 cm$^2$ area is 50 m from the speaker. a. What is the sound intensity at the position of the microphone? b. How much sound energy impinges on the microphone each second?

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball in its socket. If the mass of the eyeball is 7.5 g, a typical value, what is the effective spring constant of the musculature that holds the eyeball in the socket?

A $1.00 \mathrm{~kg}$ block is attached to a horizontal spring with spring constant $2500 \mathrm{~N} / \mathrm{m}$. The block is at rest on a frictionless surface. A $10 \mathrm{~g}$ bullet is fired into the block, in the face opposite the spring, and sticks. What was the bullet's speed if the subsequent oscillations have an amplitude of $10.0 \mathrm{~cm}$ ?

It is said that Galileo discovered a basic principle of the pendulum— that the period is independent of the amplitude—by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 5.5 s. a. How long is the lamp chain? b. What maximum speed does the lamp have if its maximum angle from vertical is 3.0°?