Tutorial 12 – Traveling and Standing Waves – Assignment The simplest standing waves that occur on a taut string are called fundamental modes, which are sinusoidal and consist of exactly one half wavelength. They oscillate with a single frequency fo that depends on the physical properties of the string: tension T, length L, and linear mass density μ. Using the appropriate relations introduced in the demonstration problem, derive the relation among those variables and answer the following questions 1. How much would you have to increase the tension to double fo? 2. How much would you have to increase the tension to raise fo 1.5 times? 3. If the string is reduced to 65% of its original length, how doesfo change? 4. If the tension increases by 25%, how much does fo increase? 5. A grand piano produces notes that vary across 8 octaves (fo differs by a factor of 2 for notes separated by one octave). If T and μ were unchanged, how much would L vary? Okay, that’s impractical, so how much would the combined ratio T/μ have to change if the lengths of all the strings were unchanged 6. Attach this page atop your solution, and turn it in by next Monday at 5:00 in the appropriate box outside SSC114. You will be graded according to the following rubric, earning either full (), partial (0), or no credit (O) on each point.