Question

On a windy day, a child standing outside a school hears the school bell. If the wind is blowing toward the child from the direction of the bell will it alter the frequency, the wavelength, or the velocity of the sound heard by the child?

Short answer

Answer: The properties of sound affected in this situation are frequency and wavelength. The frequency will increase and the wavelength will decrease due to the Doppler effect and relative motion between the child and the bell. The velocity of the sound remains unchanged.

Step-by-step solution

Understand the properties of sound

Sound is a mechanical wave that travels through a medium, such as air, by compressing particles together and creating areas of high and low pressure. The properties of sound include frequency, wavelength, and velocity. Frequency refers to the number of oscillations (vibrations) per unit of time and is measured in Hertz (Hz). Wavelength is the distance between two points in the same phase of consecutive oscillations. Velocity is the speed at which the sound travels through the medium.

Recall the Doppler effect

The Doppler effect is the change in frequency or wavelength experienced by an observer due to the relative motion between the observer and the source of the sound (in this case, the school bell). When the source and observer are moving towards each other, the frequency of the sound experienced by the observer increases and the wavelength decreases. Conversely, when the source and observer are moving away from each other, the frequency decreases and the wavelength increases.

Explain how wind affects the sound

In this situation, the wind is blowing towards the child, effectively changing the medium through which the sound travels. This causes a relative motion between the observer (the child) and the source (the school bell). Since the wind is blowing from the direction of the bell towards the child, it's as if the child is moving towards the bell.

Determine the effect on frequency, wavelength, and velocity

Using the concepts of the Doppler effect and relative motion (with the wind acting as the medium), we can deduce the changes in sound properties. Since the child is "moving" towards the source of the sound, the frequency of the sound heard by the child will increase. This also leads to a decrease in wavelength. However, the velocity of sound depends on properties of the medium in which it is traveling, such as its density and temperature. The wind's direction does not directly affect the velocity of the sound, so the velocity remains unchanged.

Summarize the result

In conclusion, when the wind is blowing towards the child from the direction of the school bell, it will affect the frequency and wavelength of the sound heard by the child. The frequency will increase and the wavelength will decrease due to the Doppler effect and relative motion between the child and the bell. The velocity of the sound remains unchanged.