Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Sound asks what oscillates, what travels, and which wave quantity is being measured.
Common stuck point:Students often know a formula related to sound but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.
Sense of Study hint:Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?
Worked Examples
Example 1
easy
Thunder is heard 6 s after lightning is seen. How far away was the lightning strike? Use the speed of sound v=340 m/s.
Answer
d≈2040 m≈2 km
First step
1
Light travels almost instantaneously, so the delay is due to the speed of sound.
Full solution
2
Use the distance formula: d=vt.
3
d=340×6=2040 m≈2 km
Sound travels much slower than light. The time delay between seeing lightning and hearing thunder can be used to estimate the distance of the lightning strike.
Example 2
medium
A sound wave in air has a wavelength of 0.5 m. What is its frequency? Is this audible? Use v=340 m/s.
Example 3
medium
A train whistle has frequency 500 Hz. Using v=340 m/s, find the wavelength and the period of the wave.
Example 4
medium
A flute note has frequency 880 Hz. Using v=343 m/s, find the wavelength to two decimal places.
Example 5
hard
Two tuning forks of 440 Hz and 444 Hz are played together. Find the beat frequency and the time between successive beats.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
medium
A person shouts toward a cliff and hears the echo 4 s later. How far is the cliff? Use v=340 m/s.
Example 2
medium
A sonar pulse is sent from a ship and the echo returns 0.8 s later. The speed of sound in seawater is 1500 m/s. How deep is the ocean floor at that point?
Example 3
easy
Can sound travel through a vacuum?
Example 4
easy
Sound is what type of wave: transverse or longitudinal?
Example 5
easy
Which sound property does frequency control: pitch or loudness?
Example 6
easy
Which sound property does amplitude control: pitch or loudness?
Example 7
easy
Sound travels in air at about 343 m/s. Is it faster or slower in water?
Example 8
easy
A sound wave has frequency 200 Hz and wavelength 1.7 m. Find its speed.
Example 9
easy
In which medium is sound slowest: solid, liquid, or gas?
Example 10
easy
Two sounds have the same loudness but one is higher pitched. What differs between them?
Example 11
medium
Sound travels at 343 m/s. A musical note has frequency 440 Hz. Find its wavelength (round to two decimals).
Example 12
medium
You shout toward a cliff and hear the echo 2 s later. Using sound speed 343 m/s, how far away is the cliff?
Example 13
medium
A bat emits sound at 50 kHz. Using sound speed 343 m/s, find the wavelength (round to four decimals).
Example 14
medium
Why does a sound seem to fade and vanish as a spacecraft leaves the atmosphere into space?
Example 15
medium
A note at 256 Hz and another at 512 Hz are played. How are their pitches related, and what is the frequency ratio?
Example 16
medium
Sound travels 1480 m/s in water. A sonar pulse returns from the seabed 0.5 s after emission. Find the seabed depth.
Example 17
medium
Why does increasing only the amplitude of a sound wave NOT change its pitch?
Example 18
medium
A sound wave has frequency 170 Hz and wavelength 2 m. Find its speed.
Example 19
medium
Sound travels at 343 m/s. How far does it travel in 3 s?
Example 20
challenge
Sound travels at 340 m/s. An organ pipe open at both ends has a fundamental wavelength equal to twice its length. If the pipe is 0.85 m long, find the fundamental frequency.
Example 21
challenge
Two sound sources play in phase, each producing amplitude 4 units at a point. Find the combined amplitude and how much louder (energy ratio, energy proportional to amplitude squared) it is than one source.
Example 22
challenge
A car horn sounds at 400 Hz. Using sound speed 340 m/s, find the wavelength, then determine how many full wavelengths fit in the 85 m to a wall.
Example 23
easy
A sound wave has speed 340 m/s and frequency 1700 Hz. Find its wavelength.
Example 24
easy
Why can astronauts on the Moon NOT hear each other's voices through the vacuum, even when only 1 m apart?
Example 25
easy
A whale song travels through ocean water at about 1500 m/s. How long does the sound take to reach a whale 4500 m away?
Example 26
easy
A tuning fork vibrates at 256 Hz. How many compressions does it send out each second?
Example 27
easy
Human hearing covers roughly 20 Hz to 20,000 Hz. Is a 15 Hz wave audible to humans?
Example 28
medium
A diver hears a boat engine 0.4 s after the surface; in air, the same sound from the same boat would reach a swimmer 1.5 s later. Using vair=340 m/s, find the swimmer's distance and the diver's distance using vwater=1500 m/s.
Example 29
medium
A wave has period T=0.004 s. Using v=340 m/s, find frequency and wavelength.
Example 30
medium
An ultrasound machine emits at 2 MHz into soft tissue where v=1540 m/s. Find the wavelength.
Example 31
medium
A starter pistol fires; an observer 680 m down the track sees the flash and hears the bang. Using v=340 m/s, find the delay between flash and bang.
Example 32
medium
Two pulses of equal amplitude 3 units travel toward each other and meet in phase. Find the combined amplitude and explain whether the original pulses are destroyed.
Example 33
medium
A sound pulse takes 1.2 s to travel from the source to a wall and return. Using v=340 m/s, find the wall's distance.
Example 34
medium
A microphone records two tones: 100 Hz and 800 Hz. Each is played at the same loudness. Compare the wavelengths in air (v=340 m/s).
Example 35
medium
An ambulance siren is heard. The driver and a stationary observer agree on what frequency the source emits. Why might the observer measure a different received frequency?
Example 36
hard
On a hot day air is warmer and sound travels slightly faster. If the speed of sound rises from 340 to 350 m/s, by what percentage does the wavelength of a 440 Hz note change?
Example 37
hard
A boy taps a long steel rail; a friend 200 m away with one ear to the rail hears two clicks. Using vair=340 m/s and vsteel=5000 m/s, find the time gap between clicks.
Example 38
hard
A pipe closed at one end and open at the other has fundamental wavelength λ=4L. If L=0.5 m and v=340 m/s, find the fundamental frequency.
Example 39
hard
Two speakers play identical tones at 340 Hz in phase. A listener stands so the path difference is 0.5 m. Using v=340 m/s, find the wavelength and predict whether the listener hears constructive or destructive interference.
Example 40
hard
A bat emits a 40 kHz chirp and the echo returns from an insect 5 m away. Using v=340 m/s, find the round-trip travel time.
Example 41
challenge
A guitar string of length 0.65 m has fundamental frequency f1=440 Hz. Find the wave speed on the string, then the wavelength and frequency of the second harmonic (n=2).
Example 42
challenge
Sound intensity falls as the inverse square of distance. If the intensity is I0 at 1 m from a point source, at what distance is it I0/100?