Standing waves

Physics 101 LO 6

1. STANDING WAVES ON VIOLIN STRINGS

2. STANDING WAVES A re stationary (as opposed to travelling waves) Vs STANDING WAVE TRAVELLING WAVE

3. STANDING WAVES Are the superposition of two harmonic waves with equal amplitude, frequency and wavelengths but moving in opposite direction v v Resulting Standing Wave from adding the two harmonic waves

4. STANDING WAVES Can be generated by plucking a string with both ends fixed Nodes are points with zero amplitudes Antinodes are points with maximum amplitudes

5. STANDING WAVES ON STRINGS Strings with two fixed ends can only produce standing waves with an integral number of half wavelength called normal modes = where L = string length n = number of antinodes = 1, 2, 3, 4, … The fundamental frequency (1 st harmonic) is the lowest frequency (longest wavelength) = The allowed frequencies are called harmonics = n n = 1, 2, 3, 4, …  

6. QUESTION PART 1 Tom wants to make a violin for his sister as a birthday present. Violins usually make sound frequencies ranging from 200~3000Hz. He has a few 30 cm long strings with linear mass densities: A 2 .8 kg/m B 4.0 kg/m C 0.62 g/m Which string should he use to make the violin in order to get a fundamental frequency of 700Hz if the tension in the string is kept at 70 N?  

7. Hints What variables are given in the question? , T, L  

8. Hints What variables are given in the question? , T, L Which equation to use when solving for linear mass density? =  

9. Solution — Tom should use string B = 700 Hz T = 70 N L = 30 cm = 0.30 m = Solve for = = = = 3.97 kg/ m 4.0 kg/m  

10. QUESTION PART 2 The violin string broke after a few weeks, but Tom doesn’t have anymore of the same string. If he uses a string with linear mass density of 4.7 kg/m, what should the tension be in the string in order to produce the same sound frequency (700 Hz)?  

11. Hints What variables are given in the question? , , L  

12. Hints What variables are given in the question? , , L Which equation to use when solving for tension? =  

13. Solution = 700 Hz = 4 .7 kg/m L = 30 cm = 0.30 m = Solve for T = T = = 4.7 kg/m = 82.9 N 83 N  

14. THANK YOU FOR WATCHING