I need help with the standing waves problems step by step

Name: Period: PHYSICS I STANDING WAVES PROBLEMS Solve the following problems using the examples given in your Standing Waves hand out. Show all steps of all formulas! 1. Melody puts a fret on her guitar string, causing it to vibrate with a fundamental frequency of 250 Hz as a wave travels through at 350 m/s. A) How long is the guitar string from the lower fixed end to the fret? B) How far and in which direction must the fret be moved in order to produce a fundamental frequency that is twice as high? 2. The fundamental frequency of a bass violin string is 1045 Hz and occurs when the string is 0.900 m long. How far from the lower fixed end of the bass violin should you place your fingers to allow the string to vibrate at a fundamental frequency 3 times as great? 3. Aaron blows across the opening of a partially filled 20.0 cm high soft drink bottle and finds that the air vibrates with a fundamental frequency of 472 Hz. How high is the liquid in the bottle? 4. John is a bass and can hit a low E that has a frequency of 82.4 Hz. Katherine is a soprano and can sing as high as the third overtone of this note. What is the highest frequency that Katherine can sing? (5 pts)Name: Period: 5. A train passes through a tunnel that is 550 m long. Assuming that the speed of sound in air is 340 m/s, what is the frequency of the vibrating air in the tunnel? 6. Cynthia, a harpist, plucks a 0.60 m long string on her harp. The string has a first overtone of 1046.6 Hz. How fast does the vibration travel through the string? 7. What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows: A) 70.0 cm B) 50.0 cm C) 40.0 cm? 8. A violin string that is 50.0 cm long has a fundamental frequency of 440 Hz. What is the speed of the waves on this string? (5 pts)