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:Pitch asks what oscillates, what travels, and which wave quantity is being measured.
Common stuck point:Students often know a formula related to pitch 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
medium
A wave on a string has speed 200 m/s and wavelength 0.25 m. Determine the pitch (frequency) of the note it produces.String wave at 200 m/s with wavelength λ = 0.25 m — what is the pitch (frequency)?
Answer
f=800 Hz
First step
1
Apply v=fλ, so f=v/λ.
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Setup·Key insight·Why it works·Common pitfall·Connection
Two organ pipes produce notes at 200 Hz and 800 Hz. How many octaves apart are they?
Example 3
hard
A wave with frequency 440 Hz in air at 343 m/s enters water, where it travels at 1500 m/s. The frequency stays 440 Hz. Find the new wavelength and explain why pitch is unchanged.
Example 4
hard
A 60 cm guitar string plays a fundamental of 200 Hz. A player presses down so that only 40 cm vibrates, with wave speed unchanged. Find the new fundamental pitch.
Example 5
challenge
A piano string of length L and tension T plays f1. To raise the pitch by exactly one octave by changing only tension, by what factor must T change? (Use v∝T at fixed L.)
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
Which property of a sound wave mainly determines its pitch?
Example 2
easy
Sound A is 200 Hz and sound B is 800 Hz. Which has the higher pitch?Compare the periods of sound A (200 Hz) and sound B (800 Hz) — which has the higher pitch?
Example 3
easy
A tuning fork vibrates 440 times per second. What is its frequency, and is its pitch the standard musical A?
Example 4
easy
If a guitar string is tightened so it vibrates faster, does its pitch go up or down?
Example 5
easy
Two sounds have the same amplitude but different frequencies. Do they have the same pitch?Both waves have the same amplitude but different periods — do they have the same pitch?
Example 6
easy
A sound has period 0.004 s. Find its frequency, which sets its pitch.A sound wave with period T = 0.004 s — find its frequency (pitch).
Example 7
easy
Does a louder sound necessarily have a higher pitch?
Example 8
easy
A bird call rises from 2000 Hz to 4000 Hz. Did its pitch rise or fall?Bird call starts at 2000 Hz (longer period) and rises to 4000 Hz (shorter period) — did the pitch rise or fall?
Example 9
medium
A wave travels at 340 m/s with wavelength 0.5 m. Find the frequency that determines its pitch.Sound wave traveling at 340 m/s with wavelength λ = 0.5 m — find the frequency (pitch).
Example 10
medium
A note at 440 Hz is raised one octave (frequency doubles). What is the new frequency?
Example 11
medium
Two strings differ only in length; the shorter one vibrates at 600 Hz, the longer at 400 Hz. Which has the higher pitch and by what ratio?
Example 12
medium
A sound's period is measured as 0.0025 s. A second sound has period 0.005 s. Which has the higher pitch?
Example 13
medium
A flute plays 524 Hz in air (340 m/s). What is the wavelength of the sound it emits?
Example 14
medium
A whistle's frequency rises from 1000 Hz to 1500 Hz. Express the pitch change as a frequency ratio.
Example 15
medium
Sound speed in helium is about 1000 m/s. A person speaks producing wavelength 0.34 m of vibration in their throat that sets the source frequency. In air (340 m/s) that frequency is 1000 Hz. What frequency reaches a listener? (Frequency is set by the source.)
Example 16
medium
Two notes are an octave apart. The lower is 256 Hz. What is the higher note's frequency?
Example 17
medium
A note of frequency 330 Hz is raised an octave, then that result is raised another octave. What is the final frequency?
Example 18
challenge
A string's fundamental is 220 Hz. Its frequency obeys f∝T with tension T. By what factor must tension change to raise the pitch by one octave?
Example 19
challenge
A car horn at 600 Hz approaches you. Using the Doppler relation f′=fv−vsv with v=340 m/s and vs=40 m/s, find the perceived pitch.
Example 20
challenge
A string fixed at both ends (length 0.5 m) vibrates with wave speed 200 m/s in its fundamental. What pitch (frequency) does it produce?
Example 21
easy
A whistle vibrates 1500 times per second. State its frequency in Hz.
Example 22
easy
A note has period T=0.002 s. Find its frequency, which determines its pitch.Period T = 0.002 s — what frequency (pitch) does this wave have?
Example 23
easy
A piano key plays a note at 262 Hz (middle C). Another key plays 524 Hz. Which has the higher pitch?
Example 24
easy
If a sound wave's period gets shorter, does its pitch go up or down?
Example 25
easy
A bat squeaks at 50,000 Hz. Is this pitch audible to humans?
Example 26
easy
A trumpet plays 880 Hz. State its period.
Example 27
medium
Sound travels at 343 m/s in air. A wave with wavelength 0.7 m has what pitch (frequency)?Sound in air (343 m/s) with wavelength λ = 0.7 m — find the frequency (pitch).
Example 28
medium
A note at 220 Hz is raised two octaves. Find the new frequency.
Example 29
medium
A note has frequency 330 Hz. A second note one octave lower has what frequency?
Example 30
medium
A flute is shortened. Does the pitch of its fundamental note rise or fall? Explain in one phrase.
Example 31
medium
A siren's frequency doubles. By what ratio does its period change?
Example 32
medium
A wave has frequency 600 Hz in air (v=343 m/s). Find its wavelength.
Example 33
medium
A 256 Hz tuning fork and a 512 Hz tuning fork are sounded together. State the octave relationship between them.
Example 34
medium
A vibrating string is held more tightly so the wave speed rises from 100 m/s to 200 m/s, with wavelength unchanged at 1 m. What happens to the pitch?
Example 35
hard
A guitar string at tension T0 plays 300 Hz. Tension quadruples and length stays fixed. Find the new pitch (use v∝T).
Example 36
hard
Two notes are 3 octaves apart. The lower has frequency 110 Hz. Find the higher.
Example 37
hard
An ambulance siren emits 700 Hz. As it approaches you at 30 m/s in air (vsound=340 m/s), what frequency do you hear? Use f′=f⋅v/(v−vs).
Example 38
hard
Same siren as before (700 Hz) now moves away at 30 m/s. Find the heard pitch with f′=f⋅v/(v+vs).
Example 39
hard
A bat emits ultrasound at 40 kHz and a moth flies away at 5 m/s (v=340 m/s). Find the frequency the moth would 'hear': f′=f(v−vo)/v.
Example 40
challenge
A car horn at 500 Hz drives toward a wall at 20 m/s (v=340 m/s). The wall reflects the sound back. Find the frequency the driver hears reflected off the wall.
Example 41
challenge
Two strings with the same length and tension differ only in linear mass density: μ2=4μ1. The first plays 600 Hz. Find the pitch of the second. (Use v=T/μ.)