MCAT Physical - Wavelength, Frequency, and Period

Waves hit a beach every three seconds. The horizontal distance between an adjacent maximum and minimum is one meter. What is the speed of the waves?

$0.67\frac{m}{s}$

$0.33\frac{m}{s}$

$3.0\frac{m}{s}$

$1.5\frac{m}{s}$

Explanation

Wave velocity is given by the product of frequency and wavelength:

$v=f\lambda$

In the question, we are given the period (waves per second). To find the frequency, we will need to take the reciprocal of the period.

$v=(\frac{1}{T})\lambda$

Using the values given in the question, we can find the velocity of the waves. The wavelength is twice the distance between adjacent maxima and minima, making our wavelength two meters.

$v=(\frac{1}{3\frac{waves}{s}})(2\frac{m}{wave})=0.67\frac{m}{s}$

Picture a transverse wave traveling through water. After the crest of one wave hits a stationary object in the water, an observer counts eight more crests hitting the same object in fifteen seconds. The frequency of the waves is __________.

0.53s-1

1.9s-1

1.9s

120s

Explanation

Right away you can rule out the answers with units in seconds, as the unit of frequency is an inverse second, or Hz. Frequency is measured in cycles per second. If eight crests pass a given point in fifteen seconds, the frequency is given by the number of crests divided by the time period.

$\frac{8}{15s} = 0.53 s^{-1}$

An electron falls from an excited state to its ground state, emitting a photon at . What is the frequency of the emitted light?

$4.11*10^{14}Hz$

$4.11*10^{5}Hz$

$2.4*10^{-6}Hz$

$2.4*10^{-15}Hz$

Explanation

The relationship between wavelength and frequency is given by the equation:

$v=f\lambda$

In this case, the velocity will be equal to the speed of light.

$v=c=3*10^8\frac{m}{s}$

Using this value and the given wavelength, we can find the frequency of the photon. Keep in mind that the wavelength must be given in meters.

$3*10^8\frac{m}{s}=f(7.3*10^{-7}m)$

$f=\frac{3*10^8\frac{m}{s}}{7.3*10^{-7}m}=4.11*10^{14}Hz$

An incandescent light bulb is shown through a glass prism. The certain wavlength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively.

What property of light does not change when it enters the prism?

Frequency

Wavelength

Velocity

More than one of these stays constant

Explanation

The frequency of light does not change when it enters a medium with a different index of refraction; in this case, that new medium is the glass of the prism. From the velocity of light equation we know the relationship between velocity and frequency.

$v = \lambda*f$

v is the velocity of light, $\lambda$ is the wavelength, and f is the frequency. When light enters the prism, its velocity changes due to the new index of refraction, but its frequency remains constant.

Because the frequency does not change, we can see that velocity is directly proportional to wavelength; thus, the shorter the wavelength, the slower the velocity. So both wavelength and velocity change when frequency is constant.

A transverse wave has a velocity of 5.2m/s. If ten cycles pass a given point in 1.6s, what are the wave’s period and wavelength?

0.16s and 0.83m

0.16s and 8.3m

6.25s and 0.83m

6.25s and 8.3m

Explanation

First calculate the frequency of the wave (cycles/sec). The problem tells us that there are ten cycles in 1.6s.

$f = \frac{10}{1.6 s} = 6.25 Hz$

Next find the period by taking the inverse of the frequency.

$\tau = \frac{1}{f} = \frac{1}{6.25 Hz} = 0.16 s$
Finally, find the wavelength by dividing the velocity by the frequency.

$v=f\lambda$
$\lambda = \frac{v}{f} = \frac{5.2 m/s}{6.25 Hz} = 0.83 m$

A stretched string of length L, mass M, and tension T is vibrating at its fundamental frequency. Which of the following changes takes place if the vibration frequency of the string increases, but tension and mass density remain constant?

Wavelength decreases

Number of nodes decreases

Velocity increases

More than one of the other options

None of the other options

Explanation

We can use the equation $v = \sqrt{\frac{T}{\frac{m}{L}}}$ together with $v = f\lambda$ . If T is constant, v cannot change assuming the mass density, m/L, is constant. Thus, $f\lambda$ must be constant; if f increases, $\lambda$ must decrease.