# Power of Sound Wave at distance

• Mnemonic
In summary, we have a sound source with a frequency of 653.8 Hz and an amplitude of 11.4 nm placed at the top of a 121.5m radio tower. Point A, which is 10.8 m above the source, is used for calculations. The air surrounding the tower has a density of 1.32 kgm-3 and sound travels through it with a velocity of 340 ms-1. The equation used is P = (1/2) ρAv (ω s( max ) )^2, where A is the area of the sound wave.
Mnemonic

## Homework Statement

A sound source is placed at the top of a (h = 121.5m) radio tower. The source has a frequency of 653.8 Hz and an amplitude of 11.4 nm at point A. The air surrounding the tower has a density of 1.32 kgm-3 and sound travels through it with a velocity of 340 ms-1. Point A is 10.8 m above the source. You may ignore any reflections of the sound from the ground.

## Homework Equations

P = (1/2) ρAv (ω s( max ) )^2

## The Attempt at a Solution

Determine angular velocity from frequency. Sub in density and velocity.
I think A means amplitude and I would put in 11.3nm.
However, s(max) is "displacement amplitude". Does this mean that s(max) = 11.4nm and A= distance from Point A to sound source?

Have been doing some research. A seems to refer to area of the wave sound. So would I be correct in putting A as 4 Pi r squared? Assuming sound is moving out as a sphere?

This is indeed the correct method for anyone else who has trouble with this question.

## 1. How does the power of a sound wave change with distance?

The power of a sound wave decreases with distance from the source. This is because as the sound wave travels, it spreads out in all directions and the energy is distributed over a larger area. As a result, the intensity or power per unit area decreases with distance.

## 2. What factors affect the power of a sound wave at a distance?

The power of a sound wave at a distance is affected by the amplitude of the wave, the frequency of the wave, and the medium through which it is traveling. Higher amplitude and frequency sound waves will have more power than lower amplitude and frequency waves. The medium through which the sound is traveling can also affect the power, as different mediums will absorb or reflect sound differently.

## 3. How is the power of a sound wave at a distance measured?

The power of a sound wave at a distance can be measured using a sound level meter. This device measures the intensity of sound in decibels (dB). The power of the sound wave can be calculated by using the sound intensity at the source and the distance from the source.

## 4. Can the power of a sound wave at a distance be increased?

The power of a sound wave at a distance cannot be increased, but it can be focused or directed using certain techniques. For example, using a megaphone or speaker can help to direct the sound in a specific direction and increase its perceived power. However, the overall power of the sound wave will still decrease with distance.

## 5. How does the power of a sound wave at a distance affect human perception?

The power of a sound wave at a distance can affect how humans perceive the sound. As the power decreases with distance, the sound may become quieter and harder to hear. This is why it is important to consider the power of sound when designing acoustically sound spaces or when using sound for communication purposes.

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