ASSIGNMENT 2 Physics 218 Due Feb 8 Spring 2008 Reading: Pain Ch 4-5. 1. A musician ﬁnds that a string on her instrument oscillates at a frequency of 435 Hz instead of the desired 440 Hz (A). She adjusts the knob at the end of the string to bring it in tune. (a) Should she increase or decrease the tension in the string to bring it in tune? (b) What is the ratio of the correct tension τ c to the initial incorrect tension τ i ? 2. Pianos have steel strings about 1 mm in diameter for middle C (261.6 Hz). The density of piano wire is ρ = 8 g/cm 3 and the maximum stress (force per unit area) that the wire can stand without breaking is about S = 8 × 10 8 N/m 2 . (Use this value for the maximum safe stress, although individual samples of wire will break at diﬀerent stresses.) (a) What should the length L of the string be if the frequency is to be 261.6 Hz? (b) How does the tension in the string compare with the weight of a 150 lb person? (c) The keys on a piano range from a low A at 27.5 Hz to a high C at 4186 Hz. If all strings
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