Question

A sinusoidal wave traveling on a string has a period of 0.20 s, a wavelength of 32 cm, and an amplitude of 3 cm. The speed of this wave is
A. 0.60 cm/s.
B. 6.4 cm/s.
C. 15 cm/s.
D. 160 cm/s.

Answer 1

Answer:

$v = 1.6 \frac{m}{s} *\frac{100cm}{1m}= 160 \frac{cm}{s}$

Explanation:

If we have a periodic wave we need to satisfy the following basic relationship:

$v = \lambda f$

From the last formula we see that the velocity is proportional fo the frequency.

For this case we have the following info given by the problem:

$T= 0.2 s, \lambda =32 cm* \frac{1m}{100cm} =0.32 m, A= 3cm*\frac{1m}{100 cm}=0.03 m$

We know that the frequency is the reciprocal of the period so we have this formula:

$f = \frac{1}{T}$

And if we replace we got:

$f =\frac{1}{0.2 s}= 5Hz$

Now since we have the value for the wavelength we can find the velocity like this:

$v = 0.32 m * 5Hz = 1.6 \frac{m}{s}$

And if we convert this into cm/s we got:

$v = 1.6 \frac{m}{s} *\frac{100cm}{1m}= 160 \frac{cm}{s}$