How Do You Calculate the Maximum Speed of a Speaker in Simple Harmonic Motion?

In summary, a loud speaker with a spring constant of N/m and an amplitude of 0.8m moves in simple harmonic motion with a frequency of (k/m)^1/2. The mass of the speaker is 90.0g and the maximum speed can be found by differentiating the sine or cosine equation for the position of the end of the spring.
  • #1
mark051
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Homework Statement



A loud speaker is connected to a string (spring constant k = N/m). The speaker moves back and forward in simple harmonic motion with an Amplitude of 0.8m. The frequency of an oscillation for amass on a string is w = (k/m)^1/2. The mass of the speaker is 90.0g.

What is the maximum speed of the speaker in m/s?

Homework Equations



Not sure which is the relevant in this situation.

The Attempt at a Solution



I found the value of w = 10.54.., however I'm not sure where to go from there. Thinking about this all week but can't work it out. The answer is 8.43m/s but how I should get this I am not sure. Any help would be really appreciated. Thanks
 
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  • #2
Welcome to PF!

mark051 said:
A loud speaker is connected to a string (spring constant k = N/m). The speaker moves back and forward in simple harmonic motion with an Amplitude of 0.8m. The frequency of an oscillation for amass on a string is w = (k/m)^1/2. The mass of the speaker is 90.0g.

What is the maximum speed of the speaker in m/s?

Hi mark051! Welcome to PF! :smile:

(have a square-root: √ and an omega: ω :wink:)

The sine (or cosine) equation will give you the position of the end of the spring …

then differentiate it to give the velocity! :wink:
 

FAQ: How Do You Calculate the Maximum Speed of a Speaker in Simple Harmonic Motion?

What is the Doppler Effect?

The Doppler Effect is a phenomenon observed in sound and light waves where the frequency of the waves appears to change when the source of the waves is moving relative to the observer.

How does the Doppler Effect work?

The Doppler Effect occurs when there is a relative motion between the source of the sound or light waves and the observer. This motion causes the wavelength of the waves to either stretch or compress, resulting in a perceived change in frequency.

What causes the Doppler Effect?

The Doppler Effect is caused by the relative motion between the source of the waves and the observer. This can be observed in everyday situations, such as the changing pitch of a siren as an ambulance approaches and passes by.

How is the Doppler Effect used in science and technology?

The Doppler Effect has many practical applications in science and technology. It is used in weather forecasting to track the movement of storms, in astronomy to measure the speed and distance of celestial objects, and in medical imaging to measure blood flow in the body.

What are the limitations of the Doppler Effect?

The Doppler Effect is only applicable to waves that are moving through a medium, such as air or water. It also only provides information about the relative motion between the source and the observer, not the absolute motion of either. Additionally, it can be affected by factors such as wind or background noise, which can make it difficult to accurately measure the frequency shift.

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