A transverse wave, frequency 15.0 Hz, travels along a string. Distance between a crest and an adjacent trough is 3.50m. What is its wavelength?

3.50m

Explanation:

the wavelength of a wave is the distance between the crest and the adjacent trough

the highest part of a wave is called the crest and the lowest part is called a trough

when the distance between the crest and the trough is vertical it is called the wave height and when its between two adjacent crests or troughs its called a wave length as well

therefore, the wavelength of the transverse wave is 3.5m

Wavelength is 7.0m

Explanation:

For a wave, while the vertical distance between its crest and trough is its wave height, the horizontal distance between two adjacent crests or troughs is its wavelength.

Do not forget that the point where the wave has the maximum height is its crest while the point where it has its minimum height.

From the foregoing, the horizontal distance between a crest and an adjacent trough will be equal to half of the wavelength (horizontal distance between two adjacent troughs or crests).

Therefore, from the question, the distance (horizontal) between a crest and an adjacent trough which is 3.50m is half of the wavelength of the wave. This implies that the wavelength of the wave is 7.0m

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft