A tuning fork vibrates at a frequency of 256 Hz. (a) When the air temperature increases, the wa

step 1 So in this question first we have to determine the changing the wavelength of sound from the tun

A tuning fork vibrates at a frequency of 256 Hz. (a) When...

A tuning fork vibrates at a frequency of $256 \mathrm{~Hz}$. (a) When the air temperature increases, the wavelength of the sound from the tuning fork (1) increases, (2) remains the same, (3) decreases. Why? (b) If the temperature rises from $0^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C},$ what is the change in the wavelength?

Key Concepts

Wave Speed

Wave speed is the rate at which a wave propagates through a medium. In the context of sound, the speed is determined by the properties of the medium (such as air) and is related to the frequency and wavelength by the equation v = f?. Thus, any change in the speed of sound due to varying conditions will directly affect the wavelength if the frequency remains constant.

Frequency

Frequency refers to the number of vibrations or cycles per second produced by a sound source, measured in hertz (Hz). For a given source like a tuning fork, the frequency is fixed, so any variation in the speed of sound results in a corresponding change in the sound's wavelength.

Wavelength

Wavelength is the distance between successive equivalent points in the wave pattern, such as from crest to crest or trough to trough. Since the relationship v = f? holds for waves, an increase in the speed of sound (with frequency constant) causes the wavelength to increase.

Temperature's Effect on Sound Propagation

Temperature has a direct effect on the speed of sound in air. As temperature increases, the energy of air molecules increases, which in turn increases the speed of sound. A commonly used approximation for the speed of sound in air is given by v ? 331 m/s + 0.6T (with T in degrees Celsius). This increase in speed with temperature leads to a longer wavelength when the source frequency is constant.

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