Pressure Wave Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Pressure Wave.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A pressure wave is a longitudinal wave made of alternating regions of higher and lower pressure moving through a medium.

Instead of crests and troughs, the medium gets squeezed and spread out as the wave passes.

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How to Use These Examples

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: Pressure Wave asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to pressure wave 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

Sound at

400 \text{ Hz}

enters water from air. In air

v = 340 \text{ m/s}

, in water

v = 1500 \text{ m/s}

. Compare wavelengths.

Answer

\lambda_\text{air} = 0.85\text{ m},\ \lambda_\text{water} = 3.75 \text{ m}

First step

Frequency is unchanged at a boundary.

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Example 2

medium

A loudspeaker emits sound at

250 \text{ Hz}

. A pressure probe sits exactly

\lambda/4

from the speaker. What is the phase difference between the speaker's vibration and the pressure at the probe?

Example 3

medium

A pressure wave at

1000 \text{ Hz}

travels in air. Compute the time delay between a compression arriving at a point and the next rarefaction.

Example 4

medium

In a closed-closed tube of length

L = 0.5 \text{ m}

, the fundamental pressure standing wave has antinodes at both ends. Find its wavelength.

Example 5

medium

A 100 Hz pressure wave in air (

v = 340 \text{ m/s}

) has a node at the rigid closed end of a tube. How far from the closed end is the first pressure antinode?

Example 6

hard

Two coherent loudspeakers

1.7 \text{ m}

apart emit pure

200 \text{ Hz}

tones in phase (

v = 340 \text{ m/s}

). A listener stands on the perpendicular bisector. Will the speakers' sounds reinforce, cancel, or partially overlap there?

Example 7

hard

Two coherent speakers

f = 680 \text{ Hz}

in air (

340 \text{ m/s}

) produce a path difference of

0.25 \text{ m}

at a listener's position. Find the phase difference in radians.

Example 8

hard

Sound intensity is given by

I = \Delta P^2 / (2\rho v)

where

\rho

is air density and

v

is sound speed. For

\Delta P = 0.6 \text{ Pa}

\rho = 1.2 \text{ kg/m}^3

v = 340 \text{ m/s}

, find the intensity.

Example 9

challenge

Two coherent in-phase speakers

1.50 \text{ m}

apart emit a

1700 \text{ Hz}

pure tone in air (

v = 340 \text{ m/s}

). A listener walks along the line connecting them. How many points of complete destructive interference (nodes) lie strictly between the two speakers?

easy

A pressure wave has frequency

500 \text{ Hz}

in air (

v = 340 \text{ m/s}

). Find its wavelength.

Example 22

easy

A sound has period

T = 0.005 \text{ s}

and travels in air at

340 \text{ m/s}

. Find its wavelength.

Example 23

easy

The distance between a compression and the next rarefaction is

0.25 \text{ m}

. Find the wavelength.

Example 24

easy

A pressure wave's amplitude is

0.5 \text{ Pa}

above atmospheric. What is its peak-to-peak pressure variation?

Example 25

easy

A sound wave's wavelength in air is

0.10 \text{ m}

and

v = 340 \text{ m/s}

. Find its frequency.

Example 26

medium

A microphone records 1200 compressions arriving in 2.0 s. Find the wave's frequency.

Example 27

medium

A 2 kHz sound in air (

340 \text{ m/s}

) reaches a wall 17 m away. After bouncing back, how long is the round trip?

Example 28

medium

A pressure amplitude is reported as

20 \text{ \textmu Pa}

above atmospheric, the conventional reference for

0 \text{ dB SPL}

. What is the SPL of a sound with pressure amplitude

2 \text{ Pa}

? Use

SPL = 20\log_{10}(\Delta P/\Delta P_{ref})

Example 29

medium

A sound wave's wavelength is

1.36 \text{ m}

in air (

340 \text{ m/s}

). Find its period.

Example 30

medium

A pressure wave is described by

\Delta P = (2 \text{ Pa})\sin(2\pi(680 t - 2x))

with

x

in metres. Find its wavelength.

Example 31

medium

Using the same wave

\Delta P = (2 \text{ Pa})\sin(2\pi(680 t - 2x))

, find the wave's speed.

Example 32

hard

Two coherent in-phase speakers separated by

0.85 \text{ m}

emit

400 \text{ Hz}

tones (

v = 340 \text{ m/s}

). A listener directly in front of one speaker (so the path difference equals the speaker separation) experiences what type of interference?

Example 33

hard

A standing pressure wave in a 1.0 m closed-closed tube has fundamental wavelength

2.0 \text{ m}

. How many pressure antinodes does the third harmonic have?

Example 34

hard

A pressure wave's amplitude triples. By what factor does its intensity change?

Example 35

challenge

A pulse with pressure amplitude

0.4 \text{ Pa}

in air (

\rho = 1.2 \text{ kg/m}^3

v = 340 \text{ m/s}

) spreads as a spherical wave from a point source. Use

I = \Delta P^2/(2\rho v)

at the 1.0 m radius. What is the source's total power (assume isotropic emission)?

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Related Concepts

Longitudinal Wave Sound

Background Knowledge

These ideas may be useful before you work through the harder examples.

longitudinal wavesound