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.