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What happens to the speed of pulses on a light vertical string when a second weight W is added without stretching the string, if the current weight W is already hanging on the string and the speed of pulses on the string is V?



The speed of pulses on a vertical string is inversely proportional to the square root of the product of tension and linear density of the string. Therefore, the new speed of pulses on the string will be V divided by the square root of 2. Using 2T for the tension of the string and m for the mass of the string, the formula that relates the speed of the pulse to tension and the linear mass density is V = sqrt(2T/m). If the tension is constant, adding the second weight W will increase the mass of the string and hence decrease the speed of the pulses. Thus the new speed is V/ sqrt(2).