 Practice Problems Vibrating Strings

Directions: On this worksheet you will be investigating the interference properties along a vibrating string and its wave velocity. omit
Question 1  If 17 meters of a type of string has a mass of 31.5 grams, what is its linear mass density? omit
Question 2  A section of this string is secured on one side of a sounding board and 40 washers are hung from its other end. If each washer has a mass of 1.50 grams, what is the tension along the string? Recall that the tension is produced by the weight of the suspended washers: weight (measured in newtons) = mass (measured in kilograms) times gravity (9.8 m/sec2). omit
Question 3  What will be the speed of any wave that travels along this string? omit
Question 4  The center of the string is now lightly plucked setting the string into vibration. If only one loop is produced along the 41.5-cm long vibrating segment, what is the wavelength of the string's frequency? Recall that a loop (N-A-N) represents one-half of a wavelength. omit
Question 5  At what frequency is the string resonating? omit
Question 6  A second string, having the same length, is now added to the sounding board. It has a linear mass density that is 3 times that of the original string. When 116 washers are added to this string and it is plucked, at what frequency will this second string resonate? omit
Question 7  How many beats would be heard between the two strings over a period of 20 seconds? Recall that one beat is heard each second when the difference in the frequencies between two sources is one hertz.