Question

You are creating a sound wave by shaking a paddle in a liquid medium. How can you increase the speed of the resulting sound wave? a) You shake the paddle harder to give the medium more kinetic energy. b) You vibrate the paddle more rapidly to increase the frequency of the wave. c) You create a resonance with a faster-moving wave in air. d) All of these will work. e) None of these will work. f) Only (a) and (b) will work. g) Only (a) and (c) will work. h) Only (b) and (c) will work.

Short answer

a) Shake the paddle harder to give the medium more kinetic energy. b) Vibrate the paddle more rapidly to increase the frequency of the wave. c) Create a resonance with a faster-moving wave in the air. d) None of the options mentioned above. Answer: d) None of the options mentioned above.

Step-by-step solution

Option (a) Analysis

Shaking the paddle harder to give the medium more kinetic energy might increase the amplitude of the sound wave but will not change the speed of the sound wave. The speed of the sound wave is dependent on the properties of the medium and not the amount of kinetic energy.

Option (b) Analysis

Vibrating the paddle more rapidly to increase the frequency of the wave will increase the frequency but will not change the speed of the sound wave. The relationship between frequency, speed, and wavelength is given by v = fλ, where f is the frequency and λ is the wavelength. Changing the frequency might change the wavelength, but the speed of the sound wave will remain constant.

Option (c) Analysis

Creating a resonance with a faster-moving wave in the air might result in a different wave pattern but will not change the speed of the sound wave in the liquid medium. The speed of the sound wave is dependent on the properties of the medium, and creating resonance with a wave in air will not change the properties of the liquid medium.

Answer

Based on our analysis of the given options, none of the options (a), (b), and (c) will work to increase the speed of the sound wave in the liquid medium. So, the correct answer is option (e) None of these will work.

Key concepts

Kinetic Energy in Waves

Kinetic energy plays a crucial role in determining the behavior of waves, including sound waves. However, it's vital to clarify that while shaking a paddle harder in a liquid might increase the wave's amplitude, it does not actually influence the speed at which the sound wave travels through the medium. The speed of sound is determined by the medium's characteristics, such as density and elasticity, as well as the temperature and pressure conditions within the medium. The kinetic energy imparted to the particles of the medium does increase the energy of the sound wave, but not its speed.
To solidify this understanding, imagine throwing a stone into a pond. Throwing a larger stone with more force creates larger ripples, or waves with greater amplitude, but those ripples don't move across the pond's surface faster. They simply have more energy. The same concept applies to sound waves in a liquid medium. Shaking the paddle harder translates to louder sounds (greater amplitudes), but the speed remains unchanged. This clear distinction is fundamental in understanding the physics of sound propagation.

Wave Frequency

Wave frequency refers to the number of wave cycles that occur in a unit of time, usually measured in Hertz (Hz), where one hertz equals one cycle per second. When discussing sound waves generated by a vibrating paddle in a liquid medium, the frequency can be increased by moving the paddle back and forth more rapidly. This action creates waves that oscillate faster, which means that the frequency is higher.
However, higher frequency does not equate to faster sound wave speed. The formula \[\begin{equation}v = f\times\lambda,\end{equation}\]where \[\begin{equation}v \end{equation}\] is the speed of the wave, \[\begin{equation}f \end{equation}\] is the frequency, and \[\begin{equation}\lambda \end{equation}\] is the wavelength, highlights this relationship. Increasing the frequency (\[\begin{equation}f\end{equation}\]) actually implies a decrease in the wavelength (\[\begin{equation}\lambda\end{equation}\]) for the wave speed (\[\begin{equation}v\end{equation}\]) to remain constant. This is because the speed of a wave is primarily governed by the medium's properties and not the wave's frequency.

Wave Resonance

Wave resonance is a phenomenon that occurs when a system vibrates at its natural frequency. For sound waves, resonance can amplify the amplitude or intensity of the wave, but it does not inherently affect the wave's speed. When creating a resonance with a faster-moving wave in air, as mentioned in the provided exercise, it pertains to matching the natural vibration frequency of the air medium to encourage the build-up of large wave amplitudes.
Understanding resonance involves recognizing that each medium has its own natural frequencies. When an external source vibrates at one of these frequencies, the waves in the medium can accumulate energy efficiently and produce a larger amplitude response. However, the energy transfer that amplifies the wave does not modify the speed at which it travels through the medium. The speed, again, is dictated by the physical properties of the medium, which remain unchanged by resonant effects. Therefore, though resonance can make waves stronger or in some cases more coherent, it cannot alter the speed of sound waves in a liquid when influenced solely by the presence of air waves.