Which sets of data show a wave with the shortest wavelength? a. speed=100 million m/s and frequency = 50 million hz. b. speed=150 million m/s and frequency=1500 hz c. speed=300 million m/s and frequency= 100 hz

The answer is A. Speed=100 million m/s and frequency = 50 million Hz.

Let's calculate for each choice the wavelength using the equation:
v = f × λ   ⇒ λ = v ÷ f

where:
v - the speed,
f - the frequency,
λ - the wavelength.

A:
v = 100 000 000 m/s
f = 50 000 000 Hz = 50 000 000 1/s (Since f = 1/T, so units are Hz = 1/s)
⇒ λ = 100 000 000 ÷ 50 000 000 = 2 m

B:
v = 150 000 000 m/s
f = 1 500 Hz = 1 500 1/s
⇒ λ = 150 000 000 m/s ÷ 1 500 = 100 000 m

B:
v = 300 000 000 m/s
f = 100 Hz = 100 1/s
⇒ λ = 300 000 000 m/s ÷ 100 = 3 000 000 m

According to these calculations, the shortest wavelength is needed for choice A.