Question

A grasshopper floating in water generates waves at a rate of 3 per second with a wavelength of 24 cm. What is the wave velocity in m/s ?The upper limit of hearing for a particular human being is 22400 Hz. What is the corresponding wavelength (in m) if the air temperature is 24°C?

Answer 1

The velocity for the grasshopper-generated waves is 0.72 m/s, while the corresponding wavelength for the upper limit of human hearing at 22400 Hz in air at 24°C is about 0.0154 m.

Step-by-step explanation:

The wave velocity can be calculated using the formula velocity (v) = frequency (f) × wavelength (λ). For a grasshopper generating waves at a rate of 3 per second with a wavelength of 24 cm, the velocity is v = 3 Hz × 0.24 m = 0.72 m/s.

For the upper limit of human hearing at 22400 Hz, the wavelength in air can also be calculated using the same formula v = f × λ, where the speed of sound in air at 24°C is approximately 346 m/s (using the approximate formula for speed of sound in air, which increases by 0.6 m/s for each degree Celsius above 0°C). Thus, wavelength (λ) = v / f = 346 m/s / 22400 Hz = 0.0154 m, which is the corresponding wavelength.

Answer 2

The wave velocity of the grasshopper waves is 0.72 m/s. The wavelength corresponding to the upper limit of hearing is 1.54 cm.

Step-by-step explanation:

The speed of a wave is determined by the product of its frequency and wavelength, as expressed by the formula: velocity = frequency × wavelength.

In the case of grasshopper waves, with a frequency of 3 waves per second and a wavelength of 0.24 meters, the velocity calculates to 0.72 meters per second.

Shifting focus to the upper limit of hearing waves, with a frequency of 22400 Hz and a known velocity (speed of sound) of 344 meters per second, the wavelength can be determined using the same formula.

This yields a wavelength of 0.0154 meters or 1.54 centimeters.

Understanding wave characteristics and calculations is fundamental in various scientific fields, including acoustics and physics.