  We analyze the power spectra of avalanches in two classes of self-organized
critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We
show that these decay with a $1/f^\alpha$ power law, where the exponent value
$\alpha$ is significantly smaller than 2 and equals the scaling exponent
relating the avalanche size to its duration. We discuss the basic ingredients
behind this result, such as the scaling of the average avalanche shape.
