Answer :
The platform should move at a rate of 48.3 m/s. This is calculated by taking the speed of sound, 344 m/s, and dividing it by the beat frequency of 7.00 Hz (which is equal to 7 beats/second). 344 m/s / 7 beats/second = 48.3 m/s.
Step 1: Calculate the wavelength of the sound wave with a frequency of 7 Hz. The wavelength is the distance a sound wave travels in a single cycle.
Wavelength = Speed of Sound (m/s) / Frequency (Hz)
Wavelength = 344 m/s / 7 Hz
Wavelength = 49.14 m
Step 2: Calculate the speed of the platform (vp) needed to detect the beat frequency of 7 Hz.
Speed of Platform (vp) = Wavelength (m) * Frequency (Hz)
Speed of Platform (vp) = 49.14 m * 7 Hz
Speed of Platform (vp) = 343.98 m/s
Therefore, the platform needs to move at a speed of 343.98 m/s for the person to detect a beat frequency of 7.00 Hz.
The speed of sound is the distance sound travels through a medium in a given amount of time. It is typically measured in meters per second (m/s). It is determined by the properties of the medium, such as temperature, pressure, humidity, and the medium itself. In air, the speed of sound is approximately 343 m/s (1,125 ft/s). In water, the speed of sound is much faster, around 1,484 m/s (4,887 ft/s).
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