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Explore the propagation of waves in a long line of people and at a baseball game. Understand wave speed, frequency, wavelength, and amplitude in various scenarios.
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Physics for Scientists and Engineers, 6e Chapter 16 – Wave Motion
In a long line of people waiting to buy tickets, the first person leaves and a pulse of motion occurs as people step forward to fill the gap. As each person steps forward, the gap moves through the line. The propagation of this gap is • transverse • longitudinal
It is longitudinal because the disturbance (the shift of position of the people) is parallel to the direction in which the wave travels.
Consider the “wave” at a baseball game: people stand up and shout as the wave arrives at their location, and the resultant pulse moves around the stadium. This wave is • transverse • longitudinal
It is transverse because the people stand up and sit down (vertical motion), whereas the wave moves either to the left or to the right.
A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string. The wave speed of the second wave is • twice that of the first wave • half that of the first wave • the same as that of the first wave • impossible to determine
The wave speed is determined by the medium, so it is unaffected by changing the frequency.
A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string. The wavelength of the second wave is • twice that of the first wave • half that of the first wave • the same as that of the first wave • impossible to determine
Because the wave speed remains the same, the result of doubling the frequency is that the wavelength is half as large.
A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string. The amplitude of the second wave is • twice that of the first wave • half that of the first wave • the same as that of the first wave • impossible to determine
The amplitude of a wave is unrelated to the wave speed, so we cannot determine the new amplitude without further information.
The amplitude of a wave is doubled, with no other changes made to the wave. As a result of this doubling, which of the following statements is correct? • The speed of the wave changes. • The frequency of the wave changes. • The maximum transverse speed of an element of the medium changes. • All of these are true. • None of these is true.
With a larger amplitude, an element of the string has more energy associated with its simple harmonic motion, so the element passes through the equilibrium position with a higher maximum transverse speed.
Which of the following, taken by itself, would be most effective in increasing the rate at which energy is transferred by a wave traveling along a string? • reducing the linear mass density of the string by one half • doubling the wavelength of the wave • doubling the tension in the string • doubling the amplitude of the wave
Doubling the amplitude of the wave causes the power to be larger by a factor of 4. In (1), halving the linear mass density of the string causes the power to change by a factor of 0.71 – the rate decreases. In (2), doubling the wavelength of the wave halves the frequency and causes the power to change by a factor of 0.25 – the rate decreases. In (3), doubling the tension in the string changes the wave speed and causes the power to change by a factor of 1.4 – not as large as in part (4).
