Question

A sine wave of amplitude $5cm$, wavelength of $3cm$ and frequency $10Hz$ moves in space what is its speed
A. $3m{s^{ - 1}}$
B. $0.3m{s^{ - 1}}$
C. $0.6m{s^{ - 1}}$
D. $0.03m{s^{ - 1}}$

Answer 1

In this question, we are provided with a sine wave with given amplitude, wavelength and frequency and we have to find the speed of the wave. It can be solved by the formula $v = \upsilon \lambda$ where we use standard symbols for wavelength and frequency. The value of amplitude was given just to confuse us.

Complete step by step answer:
Consider a sine wave having amplitude $\left( a \right) = 5cm$, wavelength $\left( \lambda \right) = 3cm$ and frequency $\left( \upsilon \right) = 10Hz$
The speed of the wave $\left( v \right)$=?
We had used the general symbols for all the above quantities. Now, using the formula $v = \upsilon \lambda$
Substituting the above values
v = 10 \times 3 \times {10^{ - 2}} \\\ \therefore v = 0.3m{s^{ - 1}} \\\
Hence, speed of the wave is $0.3m{s^{ - 1}}$

So, the correct option is B.

Additional information:
In a sine wave, wavelength is the distance between the two peaks. Amplitude of a sine wave is the maximum vertical distance reached. And frequency is the total number of complete cycles per second.Basic sine wave is represented as,
$y\left( t \right) = A\sin \left( {2\pi ft + \phi } \right)$
where $A$ is the amplitude, $f$ is the frequency and $\phi$ is the phase.

Note: The units should be taken care of. Because in the above question we are provided with the wavelength and amplitude units to be in centimeters but the standard units are meters. So, we need to change the units by multiplying by ${10^{ - 2}}$.