Question
Download Solution PDFThe speed of sound in air is 340 ms–1. If its frequency is 170 Hz, then the distance between compression and immediate rarefaction (in metres) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFKey Points
- Compression: A region in a longitudinal wave where the particles are closest together. This occurs due to the pressure increase caused by the wave.
- Rarefaction: A region in a longitudinal wave where the particles are furthest apart. This occurs due to the pressure decrease caused by the wave.
- Wavelength (λ): The distance between two consecutive compressions or rarefactions in a sound wave. It is measured in metres (m).
- Speed of Sound: The speed at which sound waves travel through a medium. In air, this is approximately 340 m/s under standard conditions.
- Frequency (f): The number of oscillations or waves produced per second, measured in Hertz (Hz).
- The speed of sound in air (v) is 340 m/s, which is a standard value for air under normal conditions.
- The frequency (f) of the sound wave is given as 170 Hz.
- The wavelength (λ) of the sound wave can be calculated using the relation: λ = v/f.
- The distance between a compression and the immediate rarefaction is half of the wavelength (λ/2).
- Formula Relation: The speed of sound is related to wavelength and frequency by the formula: v = f * λ, where:
- v = speed of sound
- f = frequency
- λ = wavelength.
- To calculate the wavelength (λ): Using the formula λ = v/f:
- Speed of sound (v) = 340 m/s
- Frequency (f) = 170 Hz
- λ = v/f = 340/170 = 2 m
- To calculate the distance between compression and rarefaction: This distance is λ/2:
- λ/2 = 2/2 = 1 m
- Thus, the distance between the compression and the immediate rarefaction is 1 metre.
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