Tension is maintained in a string as in the figure below. The observed wave speed is v = 25.0 m/s when the suspended mass is m = 3.00 kg. (You may assume that the length of the vertical portion of the string is negligible compared to the length of the string.) (a) What is the mass per unit length of the string? kg/m (b) What is the wave speed when the suspended mass is m = 1.80 kg? m/s
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![**Transcription for Educational Website:**
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**Understanding Wave Speed in Strings**
Tension is maintained in a string as shown in the figure below. The observed wave speed is \( v = 25.0 \, \text{m/s} \) when the suspended mass is \( m = 3.00 \, \text{kg} \). (You may assume that the length of the vertical portion of the string is negligible compared to the length of the string.)
[Illustration: A string passes over a pulley with a mass \( m \) hanging down on one side, keeping tension in the horizontal section of the string.]
1. **What is the mass per unit length of the string?**
\[ \_\_\_\_ \, \text{kg/m} \]
2. **What is the wave speed when the suspended mass is \( m = 1.80 \, \text{kg}? \)**
\[ \_\_\_\_ \, \text{m/s} \]
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**Explanation of the Diagram:**
The diagram shows a string that is held taut by a mass hanging over a pulley. The string passes over the pulley and extends horizontally. The tension in the string is due to the weight of the suspended mass \( m \). The problem involves calculating the wave speed along the string for different values of \( m \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1330645c-70c6-4cdc-9d97-c0134202313b%2F1a936d9f-3dfc-4aac-9cfc-15ebd17ce4de%2Fitljin_processed.png&w=3840&q=75)
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