Exam 16: Waves I

For a transverse wave on a string the string displacement is described by y(x,t) = f(x-at) where f is a given function and a is a positive constant. Which of the following does NOT necessarily follow from this statement?

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively):

A standing wave:

A long string is constructed by joining the ends of 2 shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

A string, clamped at its ends, vibrates in three segments. The string is 100 cm long. The wavelength is:

Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:

A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave?

Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are y₁(x,t) = y_msin(3x - 6t), y₂(x,t) = y_msin(4x - 8t), and y₃(x,t) = y_msin(6x - 12t), where x is in meters and t is in seconds. Match each mathematical form to the appropriate graph below.

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves CANNOT be:

When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. The speed of these waves is:

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form If the value of $\phi$ is appropriately chosen, the two waves might be:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

A wave traveling to the right on a stretched string is shown below. The direction of the instantaneous velocity of the point P on the string is:

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum velocity in m/s of any point on the string is:

The displacement of a string carrying a traveling sinusoidal wave is given by At time t = 0 the point at x = 0 has a velocity of 0 and a positive displacement. The phase constant $\phi$ is:

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

The displacement of a string is given by y(x,t) = y_msin(kx + $\omega$ t). The speed of the wave is: