Concept explainers
To rank:
The waves according to
a) their wave speed
b) the tension in the string along which they travel
Answer to Problem 1Q
Solution:
a) The waves can be ranked according to their wave speed as
b) The waves can be ranked according to their tension in the string along which they travel as
Explanation of Solution
1) Concept:
We can use the concept of the equation of transverse wave and speed of a travelling wave. The wave speed on a stretched string gives the relation between speed and tension in the string.
2) Formulae:
i)
ii)
iii)
3) Given:
The four waves along the strings with the same linear densities are
i)
ii)
iii)
iv)
4) Calculations:
a) Rank the waves according to their wave speed :
The equation of transverse wave is
The speed of the travelling wave is
The equation (i),
Compare this equation with equation (1), then the speed of the travelling wave is
The equation (ii) is
Compare this equation with equation (1), then the speed of the travelling wave is
The equation (iii) is
Compare this equation with equation (1), then the speed of the travelling wave is
The equation (iv) is
Compare this equation with equation (1), then the speed of the travelling wave is
Hence, the rank of the waves according to the wave speed is
b) Rank the waves according to tension:
The wave speed on a stretched string is
The speed on the stretched string is directly proportional to the tension in the string with the same linear density.
The speed on the stretched string for equation (i) is
The speed on the stretched string for equation (ii) is
The speed on the stretched string for equation (iii) is
The speed on the stretched string for equation (i) is
Hence, the rank of the waves according to their tension is
Conclusion:
We can find the wave speed by using its expression and rank their values. By using the expression of the speed on the stretched string, we can find thetension in each string and rank their values.
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Chapter 16 Solutions
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