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 wind blowing towards the child increases the frequency and velocity of the sound waves, but does not affect the wavelength.

Step-by-step solution

Identify the variables

First, let us identify the values of interest in this problem: frequency, wavelength and velocity. • Frequency (f) is the number of oscillations per second of the sound wave. • Wavelength (λ) represents the distance between two consecutive wave crests (or troughs) in a wave. • Velocity (v) is the speed of the sound wave in a medium (such as air). Wind can potentially affect any of these parameters, so let's examine them one by one.

Consider the Doppler effect

The Doppler effect is a phenomenon that occurs when the frequency of a wave perceived by an observer is different from the original frequency emitted by the source when there is relative motion between the observer and the source. In this case, the child standing outside is the observer and the school bell is the source. The wind is causing relative motion between the source and observer as it is blowing towards the child.

Effect of wind on velocity

When wind blows the sound waves towards the observer, it effectively changes the speed of the wave in the medium. In our case, the wind is increasing the speed of the sound wave in the air. Thus, it can be concluded that the wind does impact the velocity of the sound waves.

Effect of wind on frequency

The Doppler effect states that if the observer is moving towards the source or the source is moving towards the observer, the perceived frequency will be higher. As the wind is blowing the sound waves towards the child, the child will perceive a higher frequency. Hence, the wind does affect the frequency as well.

Effect of wind on wavelength

To assess the effect on wavelength, we can use the formula relating velocity, frequency and wavelength: v = f * λ. We have established that the frequency and velocity of the sound wave are affected by the wind. However, as velocity and frequency both increase, the wavelength remains constant because λ = v / f. As both v and f increase proportionally, the ratio (v/f) remains constant, so the wavelength is not affected by the wind. In conclusion, the wind blowing towards the child alters the frequency and velocity of the sound, but not the wavelength.

Key concepts

Understanding Sound Wave Frequency

The frequency of a sound wave is a fundamental concept that defines how often the particles of a medium vibrate when a sound wave passes through it. In more technical terms, sound wave frequency, measured in hertz (Hz), is the number of complete vibrations or cycles per second.

Imagine a school bell ringing. Each ring of the bell generates vibrations in the air, which create sound waves. These waves vibrate at a specific frequency, which determines the pitch of the sound we hear. High pitched sounds have high frequency, meaning the air particles oscillate quickly, while low pitched sounds have low frequency, with slower particle oscillations.

However, the frequency of a sound you hear can change if there's movement between you and the source of the sound. This is described by the Doppler effect. If you move towards the sound source or it moves towards you, as with wind carrying sound towards a child, the frequency increases and the sound seems higher pitched. Conversely, moving away from the source results in a lower frequency and a lower pitch.

Exploring Sound Wave Velocity

Sound wave velocity, or speed, is another essential parameter of sound wave behavior. It's defined as the distance traveled by the sound wave per unit of time, typically meters per second (m/s). The velocity of a sound wave depends on the medium it travels through—sound travels faster through solids, less fast through liquids, and slowest through gases.

However, when conditions in the medium change, such as temperature or wind speed, the velocity of sound can be altered. For instance, on a windy day, the wind can carry sound waves from a school bell to a child faster than on a still day. The wind effectively adds its own velocity to that of the sound wave, resulting in the combined velocity being higher. This change in velocity doesn't affect the intrinsic properties of the sound wave but modifies how fast it travels from source to observer, which can lead to the Doppler effect—this is why the frequency perceived by the observer can also change.

The Constancy of Sound Wave Wavelength

Wavelength is the spatial period of a wave—the distance over which the wave's shape repeats. With sound waves, the wavelength is the distance between successive crests or troughs. It's an intrinsic property of the wave and, in a uniform medium without any external force, remains constant for a given frequency and velocity.

While wind can change the velocity of sound waves and consequently affect the perceived frequency due to the Doppler effect, it doesn't alter the inherent wavelength of the sound. This is because the wavelength is the result of the interplay between frequency and velocity ($\text{wavelength}=\frac{\text{velocity}}{\text{frequency}}$). As wind increases both the velocity and frequency of sound in the same proportion, the wavelength remains unchanged. In essence, while the speed of the sound wave and its frequency can be altered by conditions like wind, the wavelength stays consistent, which speaks to the stability of this parameter under varying conditions.